In some places (esp those with low access to birth control and sub-par sexual health education), there are too many unplanned children being born to people who do not have the means to comfortably raise a child without being in poverty.

Free/low-cost birth control and better sex ed are proven to reduce these instances substantially.

If someone has the means to comfortably raise a child without being in poverty do they still need free childcare then?

Often programs like this are subsidized based on income such that if they can afford it, it is subsidized less, or you do not qualify past a certain income. That is one method of managing the program's costs, while still benefitting those who are most heavily affected. This program doesn't appear to do that, but many do.

I am not sure what point you are trying to make though.

Having an extra $2k/mo per child laying around puts you in a pretty high income bracket.

Yes. And stop bringing your kids to breweries.